Tauberian conditions for w-almost convergent double sequences |
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Authors: | Meng-Kuang Kuo |
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Institution: | (1) Center for General Education, Jen-Teh Junior College of Medicine, Nursing and Management, NO, 79-9 Sha-Luen Hu Xi-Zhou Li, Hou-Loung Town, Miaoli County, Republic of China |
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Abstract: | In this paper, we introduce the concept of w-almost convergent sequences. Such a definition is a weak form of almost convergent
sequences given by G. G. Lorentz in Acta Math. 80(1948),167-190]. We give a detailed study on w-almost convergent double
sequences and prove that w-almost convergence and almost convergence are equivalent under the boundedness of the given sequence.
The Tauberian results for w-almost convergence are established. Our Tauberian results generalize a result of Lorentz and Tauber’s
second theorem. Moreover, we prove that w-almost convergence and norm convergence are equivalent for the sequence of the rectangular
partial sums of the Fourier series of f ∈ Lp(T2), where 1 < p < ∞.
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 40A05 40B05 40E05 40G05 46B15 |
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